Not the opposite. The full group referenced here is “US citizens and certain non-US citizens whose permission to live in and work in the United States does not expire," and they went after SpaceX for discrimination against the latter (refugees and asylees, specifically).
Because those people were able to legally do some of those jobs, but SpaceX chose not to consider them because it would be more administration/bureaucracy for SpaceX. Ergo, discriminating on the basis of their status.
It was the same with disabilities, leading to the creation of the ADA. Companies would argue that they shouldn't have to hire someone in a wheelchair because it would cost them money to build wheelchair ramps and other accessibility aids.
The reality is that the regulations and restrictions in the other direction are much more severe. It's not that SpaceX cares about whom they hire; they'd hire anyone competent. The gov. will come down hard on export control and other issues if SpaceX slips up. So SpaceX essentially said fck it, just be a citizen or LPR. And this is more a sign of exasperation than anything else.
Well, they are seemingly allow to hire permanent residents and are not restricted to citizens only. If there was a citizen only requirement this would be a non issue.
You aren't allowed to exclude somebody who would otherwise be eligible because their work permit has an expiry date